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Homework Help: Quick Boolean Logic Question

  1. Jan 18, 2010 #1
    1. The problem statement, all variables and given/known data

    let p, q, and r be the following propositions

    p: You get an A on the final exam.
    q: You do every exercise in this book
    r: You get an A in this class

    translate: You get an A on the final, but you don't do every exercise in this book; nevertheless, you get an A in this class.

    2. Relevant equations

    3. The attempt at a solution

    Do I have to include the part about doing exercises at all? Since it's sufficient enough to have p[tex]\rightarrow[/tex]r to convey the message? What I'm worried about is if they want us to include it anyways so someone can go from this logic to English again. How would I include q then?

    I would assume that
  2. jcsd
  3. Jan 18, 2010 #2
    Yes, because it has a truth value and therefore affects the truth value of the whole sentence.
    But is a conjunction, so logically/grammatically it works the same way as an and.
  4. Jan 18, 2010 #3
    How about ((p[tex]\wedge[/tex]q)[tex]\vee[/tex](p[tex]\wedge[/tex][tex]\neg[/tex]q))[tex]\rightarrow[/tex]r

    Is there any way to convey this simpler?
  5. Jan 19, 2010 #4
    Using distrbutive properties, you end up with :
    (p[tex]\wedge[/tex]([tex]\neg[/tex]q[tex]\vee[/tex]q))[tex]\rightarrow[/tex]r, which is back to p[tex]\rightarrow[/tex]r, which again means a loss of the but clause.
  6. Jan 19, 2010 #5
    Wait, wasn't that my goal though? Something that simplifies to "if p then q".

    Hm, im rereading it again, and im getting the feeling that I should just word for word put it into logic. So

    (p[tex]\wedge[/tex][tex]\neg[/tex]q) [tex]\rightarrow[/tex] r

    So is their use of "but" just to confuse me?
    Last edited: Jan 19, 2010
  7. Jan 19, 2010 #6

    That's my usual assumption with these types of problems.
  8. Jan 19, 2010 #7
    Oh wow, I over-read your comment about "but" the first time through. Sorry bout that and thanks for the help.
  9. Jan 19, 2010 #8


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    Gold Member

    Yeah, exactly right.

    No, it's standard english. 'But' is the right conjunction to use, because the clause that comes after it is a negative, and tends to have the effect of lessening the impact of the first. It was your job to figure out that this sentence given in proper english is logically equivalent to:

    "You get an A in the final exam and you do NOT do every exercise in the book..."

    and you did figure it out. If somebody had said either wording to you, you would have understood what he meant.
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